Israel studying a 2-seater JSF? Well, since the US is strongly opposed to building any customised versions (for support reasons: it doesn't want to be supporting any national variants, & won't let buyers do all the support themselves), has no intention of building a 2-seater, & Israel can't build JSFs itself, that's very odd indeed.
Even if the Israelis could persuade the US to build some, they'd cost a stupendous amount, since only a few would be built. Israel would probably have to cover the full cost of development, which would gobble up a lot of the US aid it finds useful for other things.
Where did you hear this?